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COPYRIGHT DEPOSIT. 






























THE ACME 


Rapid Calculation 
Course 

BY 

HAROLD FRANKLIN HIPPENSTIEL 



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> j > 

■ >* 


THE GREGG PUBLISHING COMPANY 

NEW YORK CHICAGO BOSTON 
SAN FRANCISCO LONDON 








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W*> 


COPYRIGHT, 1923, BY THE 

GREGG PUBLISHING COMPANY 
G57-F-2 


Printed in the United States of America 


©C1A711293 

JUL 21 1923 I 


TABLE OF CONTENTS 


PAGES 

Introduction . 1-6 

General Suggestions . 7-12 

Lesson I: Addition. 13-15 

Lesson II: Addition (Contd.). 16-21 

Lesson III: Addition (Contd.). 22-25 

Lesson IV: Addition (Concluded). 26-29 

Lesson V: Subtraction. 30-31 

Lesson VI: Subtraction (Contd.). 32-34 

Lesson VII: Subtraction (Concluded)... 35-40 

Lesson VIII: Multiplication. 41-45 

Lesson IX: Multiplication (Concluded) 46-48 

Lesson X: Division. 49-52 

Lesson XI: Percentage. 53-56 

Conclusion . 57-59 
















INTRODUCTION 


THE ACME RAPID CALCULA¬ 
TION COURSE is a scientific arrange¬ 
ment of all the basic principles of addi¬ 
tion, subtraction, multiplication, and 
division, into exercises for practice, to be 
used as a complete and essential sup¬ 
plement to arithmetic and not as a sub¬ 
stitute for the elementary textbook 
which teaches the fundamental rules and 
science of arithmetic; nor for the work 
giving rules or suggestions for short cuts 
in figuring, of which there are many excel¬ 
lent methods explained in numerous text¬ 
books and treatises on mathematics. 
Therefore, before beginning this course, 
it is necessary that the person knows how 
to add, subtract, multiply, and divide. 

This course is SCIENTIFIC because 
it shows how to reach the desired at¬ 
tainment of rapid and accurate calcu¬ 
lation by the best known, quickest, and 
easiest way. 


l 


2 


RAPID CALCULATION 


The purpose of this course is to present 
a very simple and practical method 
whereby anyone, by the required effort, 
can acquire or further develop his or her 
ability to calculate rapidly and accu¬ 
rately; and eventually all figure work will 
become an easy and pleasant task, and 
at the same time be done rapidly and 
accurately. 

Many pupils of the higher grades in 
school, students in college, and particu¬ 
larly those who have gone out from school 
to work, know how to add, subtract, 
multiply, and divide, but are slow and 
inaccurate in their figure work. This is 
due principally to the lack of sufficient 
practice along lines that would develop 
their ability to a greater degree of rapidity 
and accuracy in their calculations. 

The fact that one must count on his 
fingers, or take his eyes off the figures 
and think hard, when adding, subtract¬ 
ing, multiplying, or dividing, is sufficient 
evidence that one is not familiar with 
the combinations over which he hesitates. 


INTRODUCTION 


3 


This is just what this course intends to 
help overcome. 

Many persons have wished for a simple, 
short, and efficient method that would 
help them attain this much desired 
ability, and THE ACME RAPID CAL¬ 
CULATION COURSE adequately fills 
this need. It can be used in the class¬ 
room and at home with remarkable suc¬ 
cess, and the matured business man or 
woman will find this additional training 
of great benefit. 

The ability to be expert with figures is 
invaluable to the stenographer, clerk, 
bookkeeper, accountant, business mana¬ 
ger, commercial executive, merchant, 
and any other person who is engaged in 
figure work. The person who daily adds 
incorrectly, slowly, and laboriously, small 
columns of figures in his or her work, will 
not find any help for this inefficiency in 
higher mathematics, but rather in a 
thorough familiarity with all basic forms 
of combinations entering into the four 
fundamental functions of arithmetic. 

In all calculations, whether involving 


4 


RAPID CALCULATION 


addition, subtraction, multiplication, or 
division, the result of the combination of 
certain specific figures is always the same; 
for instance, 7 plus 9 always equals 16, 
8 minus 3 always equals 5, 4 times 11 
always equals 44, 12 divided by 6 always 
equals 2. One digit or several figures 
standing alone represent that quantity 
only and at least two digits are necessary 
to cause a computation in any one of the 
four processes. All the possible com¬ 
binations that can be made with any two 
of the 9 digits and the cipher, form the 
first computations or basic combinations, 
. with or from which all further calculations 
are progressively continued. The term 
“basic combinations’* as used in this 
course will be understood to mean, in 
practically every instance, all the possible 
fundamental combinations that can be 
formed with the digits, and on which all 
further combinations of the respective 
processes are based. 

These basic combinations may either 
be found by themselves,, or enter some¬ 
where in the working out of a complex 


INTRODUCTION 


5 


problem, including several or a large 
number of combinations of one or all of 
the four processes. They have been the 
same since the invention of arithmetic, 
and will always be the same, as the 
science of arithmetic is an exact science. 

Therefore, a thorough familiarity with 
all the various basic combinations of the 
processes of addition, subtraction, multi¬ 
plication, and division, which enter into 
the working out of practical arithmetical 
problems, is the first step to accurate and 
rapid calculation, the attainment of 
which will be realized only through con¬ 
stant, systematic, and thorough practice, 
or systematic experience, as practice 
might be termed. 

The most efficient ability in handling 
figures, as well as in anything that is 
acquired, is gained only through ex¬ 
perience; that is, in the actual doing of 
the thing to be attained, and while your 
regular work or school problems will fur¬ 
nish you with practical experience, it 
is needless to say that if your experience 
is supplemented by the practice of 


6 


RAPID CALCULATION 


systematically arranged exercises which 
cover all basic forms of combinations you 
will ever meet, the result of your ex¬ 
perience naturally will be of the highest 
development obtained through a mini¬ 
mum amount of effort. 

The method used in this course is new 
only in that all the basic combinations 
which are possible, and upon which all 
progressive calculations are based, are 
systematically grouped into exercises for 
practice. 

The few exercises of the course will 
perhaps at once appear very simple and 
almost ridiculous for constant practice, 
yet they are of the most vital importance; 
although their simplicity is one of the 
main features of the course. Further, 
the course is short and the practice is 
confined to a minimum number of exer¬ 
cises, representing all the possible basic 
combinations rather than to a large num¬ 
ber of varied exercises containing fre¬ 
quent repetitions, and, therefore, it is not 
burdened with anything that is not 
absolutely essential. 


GENERAL SUGGESTIONS 


Emphasize constantly to yourself, “I 
W-I-L-L acquire the ability to calculate 
rapidly and accurately,” and then with 
determination to succeed; practice, 
PRACTICE, PRACTICE — sys¬ 
tematically, constantly, faithfully, and 
patiently, until the goal is won. 

In this course there are no complex 
problems to solve. All you need to do is 
sit down and practice systematically 
as suggested. The explanations and the 
exercises are simple, and free from tech¬ 
nicalities, so that both young and old can 
readily understand them. 

Let your practice be systematic; set 
a time when it is most convenient for 
you each day to give at least fifteen 
minutes to practicing the exercises. A 
few minutes of systematic practice daily 
will do more good than an hour or longer 
occasionally. 

Take only a few combinations at a 
time, only a small portion of an exercise 


7 


8 


RAPID CALCULATION 


if necessary, and do not attempt to hurry 
through the course. Review each day. 

First, BE ACCURATE. Rapidity will 
come through practice. Practice getting 
the results of the combinations until you 
can do so AT A GLANCE. This may call 
for the exercise of your patience, but the 
attainment of the goal will justify your 
practicing a long time if necessary. 

While several months’ faithful practice 
should show considerable development, 
and probably be sufficient for the already 
rapid and accurate calculator, no limit 
should be set upon the length of time 
but rather continue systematically and 
faithfully practicing until your ability 
to add, subtract, multiply, and divide 
rapidly and accurately with ease is 
developed to the highest possible degree. 

It seems rather astonishing, but never¬ 
theless it has been proven to be true; that 
those who calculate very rapidly are like¬ 
wise accurate. 

It is advisable to use short cuts in all 
figure work whenever practicable, but 
DO NOT use any short method in the 


GENERAL SUGGESTIONS 


practice of any of these exercises, as the 
use of any short cut method will defeat 
the purpose of this course, and the prac¬ 
tice of the exercises will not give you the 
result desired. Finish the course as 
prescribed and then take up the practice 
of essential short cuts. 

The combinations in the respective 
exercises are not all consecutively ar¬ 
ranged nor are all the answers to the 
same given. This is purposely done for 
the student’s entire benefit. Therefore, 
do not write any answer under any com¬ 
bination in the exercises. If it is neces¬ 
sary—and perhaps for some it may be 
better at first—copy the combinations 
on a separate sheet of paper with the 
correct answer, and you will be aided in 
getting the result, which is of first impor¬ 
tance. Later, discard this sheet and use 
the exercises without the written answers. 

Learn to know the figures of a basic 
combination just as you know the letters 
of a word, so that the instant you either 
seethe figures of the combination, men¬ 
tally picture them, or hear them, you can 


10 


RAPID CALCULATION 


give the correct result, in like manner as 
you immediately know a word by the 
letters that form it. In other words, the 
instant you see, picture, or hear the 
figures of a combination, they should 
immediately represent to you in the re¬ 
spective processes; the sum, the re¬ 
mainder, the product, or the quotient. 

However, your ability in handling 
figures will not be fully developed if you 
only practice the combinations as you 
see them. Learn to visualize or form a 
mental picture of each basic combination 
with the result of same, without looking 
at the printed figures. In order to 
strengthen and fully develop this faculty 
it is important that you get someone to 
read to you occasionally the various 
combinations, and as each combination 
is mentioned to you, slowly at first, 
immediately give the correct answer, 
mentally picturing the figures and the 
answer of the combination. Also, if a 
blackboard is available—it will be in 
the classroom—have a number of com¬ 
binations written on the board and then 


GENERAL SUGGESTIONS 


11 


have your assistant or the instructor 
point to the combinations at random 
while you endeavor to give the answers 
rapidly and accurately. Practice in this 
manner until you can give the answers 
almost as fast as your assistant can read 
them to you, or point to them. (In class¬ 
room work it is expected that instructors 
will realize the necessity of this practice 
and will see to it that the pupil receives 
the required oral and blackboard work.) 

Insist that your assistant, when read¬ 
ing the combinations to you, skips about 
from one combination to another instead 
of following the order given in the exer¬ 
cise, increasing the speed as your ability 
to give results quickly and correctly 
develops. 

Take the course with you; or copy an 
exercise or portion of it on a card, and 
carry this in your pocket for practice 
during your spare moments, such as when 
riding to and from school or the office. 

Finally, as mentioned before, do not 
hurry through the course. Above all, be 
systematic and accurate, and practice 


12 


RAPID CALCULATION 


only with a reasonable number of com¬ 
binations in the time you set aside or 
have available for practice, giving some 
time each day to review. Do not think 
you are wasting time in practicing these 
exercises for a year if necessary, for the 
accomplishment of a remarkable accuracy 
and rapidity in handling figures will 
amply repay you for the application of 
your time and energy. Also remember 
that a few minutes practice each day will 
benefit you much more than a long time 
spent in practicing occasionally. 


LESSON I 


TERMS 


ADDITION 

8 Addend 
4 Addend 


12 Sum or Amount 


The process of addition is used more 
in business than the other three processes 
combined and for this reason more at¬ 
tention is given to it. 

All the possible two figure combinations 
of the digits for addition are formed by 
adding each digit and the cipher to itself, 
and each digit to each of the other eight 
digits and the cipher, making 45 com¬ 
binations without the cipher and 55 with 
the cipher. As these are the first com¬ 
binations that can be formed with the 
digits for addition, and with which all 
further combinations of addition are 
formed, let us term these “basic combi¬ 
nations.’’ 


13 



14 


RAPID CALCULATION 


In Exercise No. 1 are all the possible 
combinations that can be formed with 
the digits and the cipher. Each com¬ 
bination is arranged in two ways, making 
practically two sets (one with the figures 
in inverse order to the other formation), 
of all the possible combinations of two 
figures for addition. 


Exercise No. 1. 


1 

2 

1 

3 

3 

4 

4 

2 

0 

2 

0 

2 

6 

6 

4 

5 

7 

7 

8 

1 

3 

1 

3 

5 

5 

6 

6 

4 

2 

4 

2 

8 

8 

8 

6 

7 

9 

9 

9 

3 

5 

3 

5 

7 

7 

8 

6 

6 

4 

6 

4 

0 

0 

0 

8 

9 

6 

1 

1 

5 

7 

5 

7 

8 

9 

0 

9 

8 

6 

8 

6 

2 

2 

1 

0 

1 

2 

3 

3 

7 

9 

7 

9 

0 

7 

8 

8 

0 

8 

0 

8 

4 

4 

3 

5 

6 

8 

5 

5 

9 

1 

9 

5 

1 

9 

8 

2 

1 

0 

3 

1 

6 

5 

3 

7 

4 

4 

5 

7 

3 








ADDITION 


15 


Exercise No. 1—Continued 


7 

4 

2 

3 

9 

0 

4 

3 

1 

0 

7 

4 

6 

5 

5 

6 

6 

7 

7 

0 

1 

2 

4 

5 

0 

1 

6 

5 

3 

2 

9 

8 

8 

7 

4 

4 

8 

9 

9 

0 

3 

4 

6 

7 

2 

9 

8 

7 

5 

4 

1 

0 

0 

9 

5 

9 

0 

1 

1 

2 

5 

6 

8 

9 

1 

2 

0 

9 

7 

6 

3 

2 

2 

1 

2 

3 

2 

3 

3 

4 






LESSON II 


ADDITION—Continued 

When you add a long column of figures, 
the combinations are a progression of 
those you practiced in Lesson One, and 
when you have added to 100 or over, and 
the column is still longer, you bear the 
100 “in mind” and continue adding, as 
though you started over again, until 200 
is reached, when you bear the 200 “in 
mind,” and continue adding in this 
manner. 

Naturally all the combinations that 
enter into this advanced process of ad¬ 
dition are each of the digits and the cipher 
added to each of the figures from 1 to 99. 
These combinations are all included in 
the columns in Exercise “2.” These 
columns are to be added not only once or 
twice, but again and again (several 
hundred times if necessary) as the oftener 
you add them the more familiar you will 


16 


ADDITION 


17 


become with all the possible combinations 
that enter into the adding of columns of 
figures, and consequently you will become 
more rapid and accurate. 

The following columns, therefore, con¬ 
tain all the possible combinations, with 
the exception of those with the cipher, 
that you will ever come in contact with 
in the adding of any column of figures, 
following the plan of adding to a sum of 
100 or over, and while bearing the 100 
“in mind,” continue adding as if it were 
a separate column; that is, by starting 
over again with 1 or whatever figure it 
happened to be after temoorarily taking 
off the hundreds. 

THESE COLUMNS CONTAIN 
EACH OF THE ESSENTIAL COMBI¬ 
NATIONS AND, THEREFORE, GIVE 
YOU THE MAXIMUM AMOUNT OF 
BENEFIT FROM A MINIMUM 
AMOUNT OF PRACTICE. 

Add these columns both UPWARD 
AND DOWNWARD as they must be 
added in both directions in order to get the 
practice of all the possible combinations. 


18 


RAPID CALCULATION 


Exercise No. 2 


9 12 8 6 

1 4 8 9 8 

7 5 2 7 9 

1 4 7 4 4 

12 8 15 

9 9 8 7 3 
9 2 2 4 7 

8 2 9 2 2 

2 4 4 9 1 

8 9 2 9 1 

9 117 2 

6 6 8 2 4 

4 3 4 3 6 

18 14 1 

1 8 5 2 7 

8 8 14 8 

2 3 114 

5 7 2 3 1 

2 19 9 9 

18 15 4 

3 18 5 8 

8 8 4 3 1 

_4 1 108 JL 

109 109 8 108 

3 

109 


5 1 7 2 3 7 4 

6 6 2 1 6 7 9 

8 4 3 7 4 4 3 

2 9 5 1 4 6 6 

4 8 2 2 5 2 8 

4 2 5 6 7 8 9 

2 6 3 1 8 4 1 

2 2 1 3 3 1 3 

5 4 7 6 4 9 4 

2 4 5 5 7 5 6 

7 7 5 9 3 4 5 

5 7 8 8 4 8 2 

7 5 1 4 4 3 1 

1 8 2 1 7 7 8 

3 6 9 6 8 8 7 

2 8 4 3 5 1 1 

7 4 6 6 6 4 3 

5 8 7 8 3 5 7 

9 3 4 5 6 9 3 

2 6 _ 4 8 9 _ 5 _ 6 

2 108 3 4 J_107 ^ 

9 5 9 iQ7 9 

9 2 2 107 

108 4 io7 

2 

_ 2 _ 

108 


ADDITION 


19 


Exercise No. 2—Continued 


5 7 6 2 4 

3 5 4 5 5 

3 8 3 8 7 

5 5 7 6 7 

16 17 9 

8 8 6 4 2 

3 5 4 6 3 

3 5 3 9 4 

9 2 5 1 3 

8 2 8 3 2 

2 9 3 7 6 

9 8 5 6 3 

3 14 7 5 

9 4 5 7 9 

9 5 19 9 

3 5 5 5 5 

2 7 3 6 7 

3 2 17 2 

7 7 7 105 1 
7 2 7 6 

3 _5_ 8 _J? 

_J 106 3 105 

106 A 
106 


3 113 2 8 

9 4 5 3 6 6 

6 1 2 5 7 6 

8 9 1 3 2 4 

1 4 5 3 9 7 

6 3 1 6 6 1 

2 6 5 8 9 5 

6 5 6 6 4 7 

2 4 3 5 7 6 

3 6 3 6 9 1 

3 7 8 6 1 5 

9 8 6 9 6 9 

5 7 5 7 6 8 

3 2 8 9 2 7 

3 7 6 3 7 6 

5 6 9 9 9 5 

9 9 5 4 3 4 

8 6 2 _8_ 6 3 

7 _9_ 1 103 J_ 2 

4 104 ^ 102j_ 

2 9 ioi 

M _ 7 _ 

103 


20 


RAPID CALCULATION 


While the method of grouping by tens, 
or by any other short method when add¬ 
ing, is a very good one, as is any short cut 
in figuring, yet do not use any short cuts 
in adding these columns as this will spoil 
the purpose of the exercise and you will 
not get practice in all of the possible com¬ 
binations. Use short cuts whenever and 
wherever you can in all your figure work, 
but please do not use them in the practice 
of any exercises in this course. 

Add each figure as you proceed up or 
down, without hesitation, just as if you 
were reading. Let the sum of the previous 
figures be visualized with the next figure 
to be added (which of course is all done 
in an instant), and the process continued 
without hesitation until the entire column 
is added. Through practice this becomes 
second nature and eventually addition 
becomes rapid, accurate, and easy, and 
you will be able to arrive at the result of 
a column of figures just as easy as you 
read a book; that is, without hardly any 
mental effort and without stopping to 
think for the result of a certain combi- 


ADDITION 


21 


nation, because you will be very familiar 
with all of the combinations, with their 
results, just the same as you are with the 
ordinary words of a printed page. 

Also, write these columns of figures in 
lines without changing their order and add 
them from left to right and backwards. 
This is very helpful as not all figures you 
add are found in columns. Alternate your 
practice of adding the columns and lines. 

For example, your first line would be 
your first column written as follows: 

( 109 ) 91711998289641182521 
3 8 4 ( 109 ). 


LESSON III 

ADDITION—Continued 
Many persons will be ambitious to 
learn to add three figures as well as two 
at one time at a glance. 

In the same manner as for Exercise 
“1,” Exercise “3” following contains in 
one form all the possible combinations 
that can be made with three figures, not 
including the cipher. 

The order of the figures in the com¬ 
binations can be changed so that all the 
possible combinations of three figures 
can be practiced in all the various forms 
in which they may appear. As an illus¬ 
tration, take 

3, which combi- 4 5 5 4 3 

4, nation can be 5 4 3 3 and 5 making in all 

5, made into 3 3 4 5 4 six 

-different orders of the same combination. 

Five other orders can, therefore, be made 
with the figures of each of the three figure 
combinations in this exercise on a sheet 


22 


ADDITION 


23 


of paper and practiced, if you are am¬ 
bitious to do this. However, the exercise 
as given will probably be of sufficient 
benefit if faithfully practiced. 


Exercise No. 3 


8 

4 

7 

8 

1 

2 

4 

7 

1 

4 

7 

4 

6 

1 

7 

7 

7 

1 

2 

4 

7 

2 

5 

8 

7 

7 

1 

4 

7 

8 

1 

1 

1 

1 

1 

1 

1 

5 

7 

7 

1 

6 

7 

1 

4 

7 

1 

2 

5 

7 

1 

7 

7 

3 

8 

9 

4 

7 

1 

7 

7 

7 

7 

5 

2 

8 

1 

1 

1 

1 

1 

1 

3 

4 

7 

9 

1 

1 

9 

2 

4 

6 

4 

6 

9 

1 

4 

8 

1 

2 

3 

4 

2 

4 

6 

7 

7 

7 

9 

3 

7 

8 

9 

1 

1 

2 

2 

2 

7 

9 

3 

2 

2 

2 

2 

2 

2 

7 

1 

2 

3 

6 

7 

8 

9 

2 

4 

5 

8 

1 

5 

7 

7 

7 

7 

7 

7 

7 

8 

1 

2 

5 

6 

2 

5 

6 

7 

1 

2 

3 

4 

2 

2 

2 

2 

2 

2 

5 

6 

9 

6 

9 

3 

3 

3 

4 

4 

3 

5 

7 

1 

2 

5 

7 

1 

2 

3 

6 

2 

4 

3 

5 

2 

2 

2 

2 

8 

8 

2 

3 

6 

2 

4 

8 

8 

8 

9 

3 

3 

3 

3 

4 

4 

2 

5 

6 

8 

3 

8 

9 

2 

3 

5 

8 

3 

5 

4 

7 

8 

1 

1 

8 

8 

3 

4 

6 

9 

4 

6 

8 

8 

8 

8 

3 








24 


RAPID CALCULATION 


Exercise No. 3—Continued 


3 

3 

3 

4 

4 

4 

1 

4 

5 

8 

3 

3 

3 

3 

4 

8 

1 

3 

6 

4 

7 

8 

2 

2 

4 

8 

5 

6 

1 

3 

5 

8 

8 

8 

8 

8 

5 

7 

2 

4 

4 

4 

4 

5 

8 

9 

3 

3 

3 

3 

4 

4 

2 

5 

9 

8 

9 

3 

4 

1 

2 

3 

7 

4 

8 

5 

8 

3 

8 

8 

8 

8 

5 

6 

7 

2 

8 

3 

1 

3 

4 

6 

8 

9 

4 

5 

1 

3 

4 

6 

1 

9 

9 

9 

9 

9 

9 

4 

5 

1 

3 

4 

6 

9 

1 

3 

4 

6 

8 

9 

5 

5 

6 

6 

6 

6 

9 

3 

6 

8 

1 

5 

6 

7 

6 

7 

9 

2 

3 

4 

9 

9 

9 

9 

4 

5 

6 

5 

6 

8 

9 

9 

9 

2 

5 

7 

5 

5 

5 

5 

6 

6 

6 

9 

1 

2 

5 

9 

1 

7 

9 

2 

3 

4 

6 

8 

2 

3 

6 

9 

9 

8 

5 

7 

9 

1 

2 

4 

6 

9 

9 

9 

3 

7 

5 

5 

5 

6 

6 

6 

6 

6 

8 

9 

3 

9 

5 

2 

4 

5 

7 

8 

5 

2 

4 

9 

1 

3 

9 

2 

8 

1 

2 

4 

5 

3 

9 

9 

9 

6 

8 

6 

5 

6 

6 

6 

6 

6 

5 

7 

9 

5 

5 

5 



4 

5 

7 

9 

1 

3 

4 

7 

1 

• 




9 

1 

3 

5 

6 

8 

9 

3 

9 





5 

5 

5 

5 

6 

6 

6 

6 

6 











ADDITION 


25 


Should you want to take up the prac¬ 
tice of columns containing four figures, 
all such possible combinations in one ar¬ 
rangement or order of figures can be made 
by adding each of the digits to each of 
the combinations shown above. Five 
figure combinations can be made by add¬ 
ing still another digit to each of the com¬ 
binations of four figures, and so on. 


LESSON IV 


ADDITION—Concluded 

Many persons become so proficient in 
addition as to be able to add two short 
columns of figures at a time. This is just 
a step further to more rapidity. All the 
possible two-column combinations of two 
figures are the figures 10 to 99 inclusive, 
added to each of themselves, and to each 
of the other figures from 10 to 99. In 
other words, any one of the 99 figures 
from 10 to 99 would be added to itself 
and to each of the other 88 figures, mak¬ 
ing in all nearly 10,000 combinations. 
An exercise of such a number of combi¬ 
nations is of course impracticable for 
practice in this course, but in Exercise 
“4” you will find the “cream” of all the 
possible double column two figure com¬ 
binations for practice work. There you 
will find all the possible combinations 
found in Exercise “1” so arranged as to 


26 


ADDITION 


27 


cover the principal points of these ad¬ 
vanced combinations. 


Exercise No. 4 


11 

22 

12 

33 

23 

13 

44 

19 

28 

29 

37 

38 

39 

46 

35 

25 

15 

56 

46 

36 

26 

57 

58 

59 

65 

66 

67 

68 

68 

58 

48 

38 

28 

18 

89 

84 

85 

86 

87 

88 

89 

92 

81 

71 

41 

51 

61 

101 

21 

12 

13 

16 

15 

14 

29 

18 

73 

63 

53 

43 

103 

27 

38 

33 

34 

35 

36 

47 

20 

30 

97 

74 

84 

108 

88 

72 

104 

71 

17 

28 

92 

82 

23 

56 

99 

82 

54 

95 

105 

47 

76 

91 

22 

45 

51 

65 

14 

63 

73 

38 

86 

107 

39 

57 

58 

70 

13 

62 

83 

23 

25 

35 

93 

48 

76 

85 

94 

59 

79 

29 

24 

37 

38 

39 

45 

67 


28 


RAPID CALCULATION 


Exercise No. 4—Continued 


98 

78 

91 

83 

106 

98 

85 

79 

83 

11 

32 

74 

81 

52 

34 

24 

14 

45 

88 

97 

89 

47 

48 

49 

56 

68 

69 

78 

16 

67 

57 

47 

37 

27 

17 

69 

74 

75 

76 

77 

78 

79 

79 

69 

59 

49 

39 

29 

19 

93 

94 

95 

96 

97 

98 

99 

31 

16 

102 

32 

99 

42 

52 

17 

10 

38 

27 

89 

26 

25 

62 

51 

62 

49 

84 

65 

95 

60 

50 

24 

40 

42 

54 

90 

94 

55 

56 

66 

87 

83 

75 

41 

55 

15 

64 

72 

18 

27 

77 

92 

66 

109 

49 

91 

64 

73 

19 

26 

n 

34 

21 

44 

67 

93 

74 

75 

84 

29 

96 

36 

31 

43 

53 

80 

12 

61 


ADDITION 


29 


Exercise No. 4—Continued 

96 87 78 69 95 86 77 

59 58 57 56 49 48 47 

65 68 

16 46 

Double columns of three, four or more 
figures can be made for practice, if de¬ 
sired, and it is suggested, that the com¬ 
binations in Exercise No. 3 be used for 
three figure double column exercises. 


LESSON V 

SUBTRACTION 

{ 7 Minuend 
3 Subtrahend 
4 Remainder or Difference. 

In Exercise No. 5 you will find all the 
possible basic combinations of subtrac¬ 
tion, both in subtracting a lesser from a 
greater number, and also in subtracting a 
greater digit from a lesser digit increased 
10 units by “borrowing.” 

Practice these exercises until you can 
give the remainder of each at a glance, 
with ease, and without error. Then it is 
only a matter of continued systematic 
practice until the desired rapidity is 
attained. 

To prove subtraction, the sum of the 
remainder and the subtrahend must 
equal the minuend. 


30 


SUBTRACTION 


31 


Exercise No. 5 


7 

9 

14 

6 

8 

7 

7 

4 

11 

15 

2 

3 

9 

2 

6 

4 

7 

3 

2 

7 

13 

10 

1 

3 

5 

12 

5 

9 

10 

16 

6 

0 

1 

2 

3 

9 

1 

4 

4 

9 

10 

13 

15 

12 

18 

6 

4 

3 

7 

8 

3 

5 

8 

6 

9 

3 

2 

3 

6 

4 

13 

2 

6 

8 

9 

17 

9 

10 

17 

9 

8 

1 

6 

3 

2 

9 

0 

5 

8 

1 

9 

2 

10 

7 

4 

5 

8 

11 

12 

16 

5 

2 

9 

5 

1 

0 

2 

3 

5 

7 

10 

7 

14 

5 

2 

4 

9 

6 

10 

15 

1 

3 

5 

2 

0 

4 

7 

1 

2 

9 

13 

4 

8 

11 

1 

9 

8 

7 

14 

12 

9 

0 

8 

8 

0 

9 

5 

1 

6 

8 

11 

12 

10 

5 

6 

9 

7 

16 

3 

8 

9 

3 

8 

5 

4 

6 

0 

8 

1 

0 

13 

11 

3 

5 

10 

6 

11 

8 

8 

6 

4 

5 

0 

4 

7 

„ 5 

7 

7 

1 

0 

15 

12 

14 

11 

11 

13 

9 

10 

12 

14 

6 

4 

7 

6 

4 

7 

8 

6 

7 

8 












LESSON VI 


SUBTRACTION—Continued 

As a supplement to Lesson No. V, 
Exercise “6” furnishes practical examples 
of subtraction and at the same time gives 
excellent practice in such a way as to 
cover all the BASIC forms of subtraction, 
WITHOUT DUPLICATION; thereby 
giving a maximum amount of benefit 
from a minimum amount of effort. 

In the operation of subtraction, when a 
greater number is to be taken from a lesser 
figure, it becomes necessary to take or 
borrow “1” or 10 units from the next 
preceding figure of the minuend. All 
possible combinations resulting from this 
operation are included in the arrange¬ 
ment of these exercises. Both the taking- 
away and the making-up methods may 
be used in the practice of these exercises. 


32 


SUBTRACTION 


33 


Exercise No. 6 


91 

57 

76 

93 

86 

74 

95 69 

46 

90 

32 

43 

72 

44 

61 

54 15 

40 

19 

58 

65 

29 

94 

37 

82 38 

47 

10 

23 

51 

11 

63 

30 

80 21 

31 

73 

87 

99 

49 

75 

98 

78 59 

84 

70 

35 

18 

13 

52 

27 

25 14 

62 

89 

64 

92 

88 

79 

56 

97 28 

66 

17 

60 

81 

26 

16 

41 

36 20 

42 

96 

39 

85 

68 

55 

83 

48 67 

77 

45 

12 

53 

24 

50 

71 

22 33 

34 

207 

390 

516 

962 

2200 

645 

302 

037 

293 

347 

288 

1202 

159 

082 

910 

536 

6001 

503 

480 

714 

833 

819 

149 

0901 

073 

384 

565 

476 

9 52 

1021 

1031 

942 

912 

813 

427 

387 

793 

694 

486 

783 

674 

139 

863 

640 

1061 

318 

760 

922 

744 

179 

546 

397 

129 

667 

684 

268 

734 

1008 

823 

615 

724 

1081 

972 

367 

048 

575 

456 

466 

199 

189 
















34 RAPID CALCULATION 

Exercise No. 6 —Continued 


570 

625 

932 

475 

357 

585 

417 

1030 

1051 

238 

931 

0496 

905 

1041 

853 

015 

595 

278 

526 



248 




1071 

754 

404 

298 

169 

064 

850 

1011 

709 

758 

892 

059 

635 

843 

806 

258 

377 

026 












LESSON VII 


SUBTRACTION—Concluded 

The making-up method as a process of 
subtraction is of valuable use in the mak¬ 
ing of change, not only to the cashier 
or clerk, but to the purchaser as well, in 
order to quickly check up the amount of 
the change handed to him, for no doubt 
nearly every one has experienced a loss 
through the unintentional mistake of a 
clerk. 

Instead of taking away a certain num¬ 
ber from another one, by the making-up 
method you add to the number usually 
taken away the figure or figures which 
make up the difference to the whole 
number. 

For instance, as in “making change,” 
suppose an article costs you 23 cents 
and you hand the clerk a 25 cent piece. 
Your change would be 2 cents because 
23 plus 2 equals 25. Or, say you gave a 


35 


36 


RAPID CALCULATION 


$1. note, the difference due would be 77 
cents and your change should total that 
amount. 

In another way you would not have to 
count your change to see if you had 77 
cents, but in making the change you 
would say “23 (as the cost price), 25, 50, 
$1.00,” by handing out respectively 2 
cents, a 25 cent piece, and a 50 cent piece. 
Whatever the value of the coins were you 
would add the represented amount of 
each coin as you passed them out or they 
were handed over to you. 

The combinations in this lesson con¬ 
tain practically every combination of 
importance in the “making change” 
method, and a thorough familiarity with 
them will add greatly to your ability to 
calculate rapidly, as well as counting 
your change or making it promptly and 
accurately. 

Practice these combinations both by 
giving the full amount required to make 
up the difference between the figure given 
and the total, and also by “making 
change.” For instance, in 61 plus? 


SUBTRACTION 


37 




equals 70; first, give your answer as 
“9”; second, give your answer as “61, 
65, 70,” while mentally adding respec¬ 
tively 4 cents and 5 cents. Where there 
is a greater difference more change of 
course is involved in the “making-up.” 

Exercise No. 7 


1 + 
31 + 
57+ 
82+ 
2 + 
32+ 
62+ 
88 + 
7+ 
37+ 
63 + 
93 + 
13+ 
38+ 
68 + 
54+ 
14 + 
43 + 
74 + 
59 + 
19 + 
49 + 


= 5 
= 35 
= 65 
= 85 
= 10 
= 40 
= 65 
= 95 
= 10 
= 40 
= 70 
= 95 
= 15 
= 45 
= 70 
= 75 
= 20 
= 45 
= 80 
= 75 
= 20 
= 55 


30+ 
56 + 
81+. 

1 + 
31 + 
61 + 
87+ 

6 + 
36+ 
62+ 
92+ 
12 + 
37+ 
67+ 
53 + 
13+ 
42+ 
73 + 
58+ 
18 + 
48+ 
78+ 


= 35 
= 65 
= 85 
= 10 
= 40 
= 65 
= 95 
= 10 
= 40 
= 70 
= 95 
= 15 
= 45 
= 70 
= 75 
= 20 
= 45 
= 80 
= 75 
= 20 
= 55 
= 80 


S8 


RAPID CALCULATION 



Exercise No. 

79+ =80 

64+ =75 

25+ =30 

54+ =55 

85+ =90 

69+ =75 

26+ =35 

55+ =60 

76+ =85 

74+ =75 

59+ =60 

80+ =85 

4+ =5 

34+ =35 

60+ =65 

86 + =95 

5+ =10 

35+ =40 

61+ =70 

91+ =95 

11+ =15 

36+ =45 

66 + =70 

52+ =75 

12 + =20 
41+ =45 

72+ =80 

57+ =75 

17+ =20 


7—Continued 

63+ =75 

24+ =30 

53+ =55 

84+ =90 

68 + =75 

29+ =30 

54+ =60 

89+ =90 

73+ =75 

58+ =60 

79+ =85 

3+ =5 

33+ =35 

59+ =65 

84+ =85 

4+ =10 

34+ =40 

64+ =65 

90+ =95 

9+ =10 

39+ =40 

65+ =70 

51+ =75 

11+ =20 
40+ =45 

71+ =80 

56+ =75 

16+ =20 
46+ =55 






SUBTRACTION 


39 


Exercise No. 7 — Continued 


47+ 

= 55 

76+ 

= 80 

77+ 

= 80 

61 + 

= 75 

62+ 

= 75 

22+ 

= 30 

23 + 

= 30 

51 + 

= 55 

52+ 

= 55 

82+ 

= 90 

83+ 

= 90 

66+ 

= 75 

67 + 

= 75 

27+ 

= 30 

28+ 

= 30 

52+ 

= 60 

53 + 

= 60 

87+ 

= 90 

88+ 

= 90 

71 + 

= 75 

72+ 

= 75 

28 + 

= 35 

29 + 

= 35 

57+ 

= 60 

78 + 

= 85 

77+ 

= 85 

2+ 

= 5 

55 + 

= 75 

32+ 

= 35 

15 + 

= 20 

58 + 

= 65 

44 + 

= 45 

83 + 

= 85 

75 + 

= 80 

3+ 

= 10 

60+ 

= 75 

33+ 

= 40 

21 + 

= 30 

63+ 

= 65 

50+ 

= 55 

89 + 

= 95 

81 + 

= 90 

8+ 

= 10 

65 + 

= 75 

38+ 

= 40 

26+ 

= 30 

64+ 

= 70 

51 + 

= 60 

94 + 

= 95 

86 + 

= 90 

14 + 

= 15 

70 + 

= 75 

39 + 

= 45 

27+ 

= 35 

69 + 

= 70 

56 + 

= 60 


40 


RAPID CALCULATION 


In addition to the combinations given 
above, the following combinations should 
be written out and also practiced, as the 
above list is not complete without them: 

Twenty-four combinations, from 1 plus 
? equals 25, up to 24 plus ? equals 
25. Fifty combinations, from 1 plus ? 
equals 50, up to 49 plus ? equals 50. 
One hundred combinations, from 1 plus 
? equals 100, up to 99 plus ? equals 
100 . 

These combinations will then cover 
every item of change in denominations 
of $1.00 and below and naturally cover 
fractions of a dollar above one dollar. 


LESSON VIII 


MULTIPLICATION 

{ 15 Multiplicand 

_7 Multiplier 

105 Product 

The multiplication table is taught in 
all schools to such an extent that prac¬ 
tically every one should be able to repeat 
it accurately and without hesitation. If 
you cannot do this it is suggested that you 
again familiarize yourself with it. Then 
continue with Exercise “8” which con¬ 
tains all the combinations that are found 
in the multiplication table up to and 
including the 9th table. 

In a problem requiring the multipli¬ 
cation of figures progressively, there is, 
when the product is greater than 9, a 
figure to carry over and to be added to 
the product of the next combination. 

To explain; let us take the example 
527 x 8. The first operation is 8 x 7 equal- 


41 


42 


RAPID CALCULATION 


ling 56. The “6” is set down as a figure in 
the product and the “5” is carried over to 
be added to the product of 8 x 2, which 
plus the “5” carried over makes a total 
of 21. The “1” of this result is placed in 
its proper place in the answer and the 
“2” is carried over to be added to the 
product of 8 x 5, or 40, making 42, which 
figures are placed in the answer. 

If you have mastered the multiplica¬ 
tion table, you should have no difficulty 
in giving the products of all the possible 
multiplication combinations, but you may 
feel that you do not add to the subse¬ 
quent product the amount carried over, 
as rapidly as you desire. 

To overcome this little difficulty the 
combinations in Exercise “8” are ar¬ 
ranged so that all the figures which are 
possible to be carried over and added to 
the respective products in the operation 
of the first nine multiplication tables, 
will be given. 

The faithful systematic practice of 
these combinations should naturally de¬ 
velop any person’s ability to multiply 


MULTIPLICATION 


43 


with remarkable ease, accuracy and 
rapidity. 

Exercise No. 8 


9X2+2 
9X9+7 
8X6+6 
9X1+4 
7X4+5 
9X6+6 
6X3+3 
9X9+8 
5X7+1 
9X1+3 
4X8+2 
9X2+3 
3X5 + 1 
9X3+3 
2X1 + 1 
3X3+1 
4X1+3 
8X8+7 
7X6+6 
5X1+4 
7X3+3 
4X2+3 
8X8+1 
4X9+3 
3X9 + 1 
8X9+6 
7X8+5 


2X4+1 
8X9+3 
9X7+7 
7X1 + 1 
9X6+7 
6X4+4 
9X8+8 
5X2+2 
9X3+4 
2X2+1 
9X1+8 
3X3+2 
9X7+8 
3X8+1 
9X6+8 
6X8+5 
3X4+2 
4X4+3 
8X1 + 1 
7X7+6 
6X6+5 
5X1 + 1 
8X9+7 
7X4+4 
6X1+5 
8X8+6 
7X4+6 


9X1 + 1 
2X3+1 
9X5+5 
3X4 + 1 
9X1+6 
3X8+2 
9X5+8 
4X2+2 
9X9 + 1 
4X5+3 
9X1+2 
5X3+4 
9X3+5 
6X1 + 1 
9X9+2 
4X6+3 
5X2+3 
3X5 + 2 
8X9+1 
5X5+2 
8X9+2 
5X5 + 1 
8X2+2 
5X1+2 
8X3 + 6 
6X7+1 
4X6+1 


44 


RAPID CALCULATION 


Exercise No. 8—Continued 


5X3+3 
6X2+4 
8X9+5 
8X3+7 
6X5+5 
8X4+4 
4X3+3 
6X9 + 1 
6X7+3 
8X2+5 
7X3+4 
5X7+3 
6X8+1 
5X2+4 
9X9+3 
4X4+2 
7X9+6 
4X5+1 
9X5+6 
4X7+3, 
9X4+5 
5X4+4 
6X1+2 
8X4+5 
9X4+8 
3X6+1 
5X5+4 
4X7+2 
9X3+8 


4X4 + 1 
5X5+3 
8X1+7 
8X4+6 
7X1+2 
8X5+5 
6X6+1 
4X6+2 
8X2+6 
7X3+5 
6X7+4 
7X9+2 
5X8+1 
2X5+1 
4X9 + 1 
9X9+4 
4X7+1 
2X6+1 
7X9 + 1 
9X5+7 
4X8+3 
9X4+6 
8X5+6 
2X7+1 
8X6+7 
9X3 + 6 
7X1+4 
2X8+1 
6X1+4 


7X2+2 
8X9+4 
5X6+2 
8X8+2 
3X9+2 
8X1+6 
6X3+4 
8X8+3 
7X3+6 
6X7+5 
7X9+3 
7X7+5 
5X8+2 
9X9 + 6 
3X1 + 1 
4X5+2 
7X9+5 
9X9+5 
3X6+2 
5X8+4 
9X4+4 
4X8+1 
9X4+7 
3X1+2 
6X2+3 
8X4+7 
9X3+7 
5X7+4 
7X1+3 


MULTIPLICATION 


45 


Exercise No. 8—Continued 


8X8+4 

9X2+5 

5X6 + 1 

5X6+4 

7X1+5 

9X2+6 

6X1+3 

8X3+3 

3X2 + 2 

8X5+7 

2X9 + 1 

6X2+2 

9X2+7 

7X1+6 

4X9+2 

3X7+1 

9X1+5 

7X8+6 

5X9+4 

7X2+4 

9X2+8 

7X8+1 

8X7+7 

3X7+2 

4X1 + 1 

7X2+6 

7X8 + 3 

7X2+3 

8X1+2 

5X7+2 

8X8+5 

5X6+3 

6X2+5 

9X1+7 

8X3+4 

4X1+2 

5X1+3 

6X3+5 

5X9+2 

7X8+2 

7X7+2 

8X2+3 

6X6+3 

8X3+5 

6X6+2 

8X1+3 

6X9+3 

7X8+4 

6X7+2 

7X9+4 

8X2+4 

7X7+1 

8X1+5 

6X4+5 

8X1+4 

6X6+4 

7X2+5 

6X8+2 

6X8+4 

7X7+3 

7X5+5 

5X9+1 

6X9+4 

8X2+7 

7X5 + 6 

9X2+4 

6X8+3 

6X9+2 

7X7+4 

5X8+3 

5X9+3 

6X9+5 


LESSON IX 


MULTIPLICATION—Concluded 

For those who desire a further and 
more practical application of the combi¬ 
nations in Exercise “8,” the following 
exercises are arranged so that all the pos¬ 
sible combinations shown in Lesson 
VIII come into the process of multiply¬ 
ing in those exercises. 

Multiply each set of figures by each of 
the digits from 2 to 9 respectively, multi¬ 
plying oftener with the most difficult 
digit. These exercises can be used as the 
multiplicand for figures higher than 9, 
although such practice would not contain 
all the combinations resulting from using 
those figures, as these exercises are ar¬ 
ranged only for use with the digits. 

Exercise No. 9 

911 812 713 614 515 416 

X X X X x x 


46 


MULTIPLICATION 


47 


Exercise No. 9—Continued 


823 

724 

625 

526 

427 

328 

X 

X 

X 

X 

X 

X 

735 

636 

537 

438 

339 

603 

X 

X 

X 

X 

X 

X 

647 

548 

449 

704 

451 

352 

X 

X 

X 

X 

X 

X 

559 

405 

561 

462 

363 

264 

X 

X 

X 

X 

X 

X 

671 

572 

473 

374 

275 

176 

X 

X 

X 

X 

X 

X 

583 

484 

385 

286 

187 

988 

X 

X 

X 

X 

X 

X 

495 

396 

297 

198 

999 

309 

X 

X 

X 

X 

X 

X 

317 

218 

119 

801 

121 

922 

X 

X 

X 

X 

X 

X 

229 

902 

231 

132 

933 

834 

X 

X 

X 

X 

X 

X 

341 

242 

143 

944 

845 

746 

X 

X 

X 

X 

X 

X 


48 


RAPID CALCULATION 


Exercise No. 9—Concluded 


253 

X 

154 

X 

955 

X 

856 

X 

757 

X 

658 

X 

165 

X 

966 

X 

867 

X 

768 

X 

669 

X 

506 

X 

977 

X 

878 

X 

779 

X 

107 

X 

781 

X 

682 

X 

889 

X 

208 

X 

891 

X 

792 

X 

693 

X 

594 

X 

110 

X 

220 

X 

330 

X 

440 

X 

550 

X 

660 

X 


770 880 990 

XXX 


Eight sets of these figures may be 
written and each of the digits placed as 
the multiplier for each set, thereby mak¬ 
ing a complete set of exercises for each 
digit always at hand for instant practice. 


LESSON X 


DIVISION 


TERMS 


Divisor 3)963 Dividend 
Quotient 321 


Division by the short or mental 
method is generally done up to including 
the figure 12 as the divisor. From 13 up 
the long division method is generally 
used, although some persons do use the 
short method for some figures higher than 
12, and should when such division is fre¬ 
quently used in one’s line of work. 

The long division method involves 
principally the processes of multiplica¬ 
tion and subtraction, and, therefore, 
proficiency in multiplication and sub¬ 
traction will also insure proficiency in 
long division. 

In short division the multiplication table 
itself comes into the work, and also the 
process of subtraction where the dividend 
is greater than the product of the divisor 


49 



50 


RAPID CALCULATION 


and the respective figure of the quotient. 
For instance, in the example 9)79, the 
largest divisible product is that of the 
quotient 8 times the divisor 9, or 72, 
which subtracted from 79 leaves a re¬ 
mainder of 7. All such possible basic 
divisible combinations are to be found in 
Exercise No. 10. 

To prove division, multiply the divisor 
by the quotient, adding the remainder, if 
any, which result should equal the dividend. 

0 T Exercise No. 10 

Scheme. 


Divide 

2 into 

all the fig. from 

2 to 

19 

inch 

a 

3 

a 

U 

a 

u 

u 

3 “ 

29 

u 

a 

4 

a 

u 

u 

u 

a 

4 “ 

39 

u 

u 

5 

a 

a 

u 

a 

u 

5 “ 

49 

« 

u 

6 

u 

u 

a 

u 

u 

6 “ 

59 

u 

a 

7 

a 

u 

a 

a 

a 

7 “ 

09 

u 

a 

8 

u 

u 

a 

u 

« 

8 « 

79 

u 

u 

9 

u 

u 

u 

a 

u 

9 “ 

89 

a 

a 

10 

u 

a 

u 

a 

a 

10 “ 

99 

a 

a 

11 

u 

u 

a 

u 

a 

11 “ 

1C9 

a 

u 

12 

u 

u 

u 

u 

u 

12 “ 

119 

u 


)10 

)80 

)30 

)40 

)50 

Hi 

)21 

)31 

)41 

M 

)12 

)22 

)32 

)42 

)52 


DIVISION 


51 


Exercise No. 10—Continued 


H 

)13 

)23 

)33 

)43 

)53 

)4 

)X4 

)24 

)34 

)44 

)54 

H 

)15 

)25 

)35 

)45 

)55 

H 

)16 

)26 

)36 

)46 

)56 

YL 

HZ 

)27 

)37 

)47 

HZ 


)18 

)28 

)38 

)48 

>58 

H 

)19 

)29 

)39 

)49 

)59 

)C0 

)70 

)80 

)90 

)100 

)110 

)61 

)71 

)81 

)91 

)101 

)1H 

)62 

)72 

)82 

)92 

)102 

)112 

)63 

)73 

)83 

)93 

)103 

)113 

)64 

)74 

)84 

)94 

)104 

)114 

)65 

)75 

)85 

)95 

)105 

) 115 

)66 

)76 

)86 

)96 

)106 

) 116 






RAPID CALCULATION 




52 


Exercise No. 10—Continued 


)67 

)77 

)87 

)97 

)107 

)117 

)68 

)78 

)88 

)98 

)108 

)118 

)69 

)79 

)89 

)99 

)109 

)119 











LESSON XI 


PERCENTAGE 

Your next and last task now is to take 
up the practice of short cuts, and also the 
compilation and practice of any special 
combinations used in your figure work 
and which will be of help to you. This 
will put the finishing touches on your 
ability to calculate to the highest degree 
of rapidity, accuracy, and ease in your 
particular line of work. 

As short cut methods are generally 
explained in advanced arithmetic books 
and in numerous other works on the 
subject, which can be obtained at almost 
any good book store or probably in school, 
there is no need to refer to or describe 
any of the methods in this course. 

If your figure work is, or will be, of a 
special character, all the possible funda¬ 
mental or basic combinations which enter 
into it should be worked out and gathered 


53 


54 


RAPID CALCULATION 


together into an exercise and practiced, 
and soon you will find that such combi¬ 
nations are handled with ease and become 
“second nature” just as the basic combi¬ 
nations of this course should be at the 
“tip of your tongue” always at your 
command. 

Practically every kind of business, 
trade, or profession, has a special char¬ 
acteristic method of figuring applicable 
to that particular kind of business, but 
this does not in any way affect the func¬ 
tions of addition, subtraction, multi¬ 
plication and division. 

The various methods of figuring used in 
different kinds of businesses are too 
numerous to give any attention to them 
here, but as you now understand the 
method of this course, you should be 
able to make up exercises of all the prin¬ 
cipal and basic combinations that you 
constantly use in your particular figure 
work, and which you feel you should be 
more familiar with. 

As an illustration, let us assume that 
it is essential for you to know and use per- 


PERCENTAGE 


55 


centages and their equivalents in common 
fractions. We will then prepare a memor¬ 
andum about as follows: 


TERMS: 


(Numerator 
\ Denominator 


2 

3 


To find the equivalent of a fraction in 
percentage, divide the denominator into 
the numerator after a decimal and two 
ciphers have been added to the numera¬ 
tor, and the result will be the terms of 
the fraction expressed in percent; as, 


3 _ 4 )3.00 
i ~ .75 or 75% 


To change a percentage into a fraction, 
the figures of the percent represent the 
numerator and 100 equals the denomina¬ 
tor: as 

75 

75% equals - which reduced equals % 


The following are the most common 
fractions and percentages used, and they 
should be learned so that they are—so to 
speak—at the “tip of your tongue.” 



56 


RAPID CALCULATION 


Exercise No. 11 


1/50 — 2% 

1/40 — 2-1/2% 
1/32 — 3-1/8% 
1/25 — 4% 

1/20 — 5% 

1/16 — 6-1/4% 
1/15 — 6-2/3% 
1/12 — 8-1/3% 
1/10 — 10 % 

1/9 — 11-1/9% 
1/8 — 12-1/2% 
1/7 — 14-2/7% ' 
1/6 — 16-2/3% 
3/16 — 18-3/4% 
1/5 — 20% 

1/4 — 25% 

15/16 — 


5/16 — 31-1/4% 
1/3 — 33-1/3% 
3/8 — 37-1/2% 
2/5 — 40% 

7/16 — 43-3/4% 
1/2 — 50% 

9/16 — 56-1/4% 
3/5 — 60% 

5/8 — 62-1/2% 
2/3 — 66-2/3% 
11/16 — 68-3/4% 
3/4 — 75% 

4/5 — 80% 

5/6 — 83-1/3% 
13/16 — 81-1/4% 
7/8 — 87-1/2% 
93-3/4% 


Combinations for figuring interest, and 
many other classes of figuring can be 
worked out to advantage, and little 
practice in at least the frequent combina¬ 
tions will develop your ability more than 
you can realize at the moment. 


CONCLUSION 


I want to emphasize again the impor¬ 
tance of mastering these fundamental 
combinations as all further arithmetical 
calculations are only progressive steps of 
these basic combinations. They are very 
closely related, subtraction being the 
inverse of addition, and short division the 
inverse of multiplication, etc. 

Review these exercises daily, if possible, 
and if you find you are not quite as 
proficient in some of the combinations, 
you should give more attention to them 
so that your proficiency in ALL the fore¬ 
going combinations will be one hundred 
percent. 

Naturally, the more application you 
give to the exercises of this course, the 
more developed will be your ability. 
Even after you have finished the course 
you will sometimes want to review 
occasionally in order to keep in trim, 
just as the pianist practices finger 
exercises in order to keep on playing well. 

Of course you want to develop your 


57 


58 


RAPID CALCULATION 


ability to handle figures to the highest 
possible degree of rapidity and accuracy, 
and the quickest and easiest way to the 
acquirement of this ability is the con¬ 
tinued practice of these basic combina¬ 
tions. There is no “Royal Road to Suc¬ 
cess” in figures nor in any other worthy 
attainment. Also remember that the 
man with the large earning capacity is 
the one that can do his work accurately 
and quickly, and with such ease as to 
consider it like playing. 

The Combinations in Exercises 2, 4, 6, 
and 9 are not to be memorized, as they 
are arranged solely for giving practice in 
the basic combinations, but the RE¬ 
SPECTIVE BASIC COMBINATIONS 
SHOULD BE KEPT CONSTANTLY 
IN MIND IN THE PRACTICE OF 
THESE EXERCISES. 

Exercises 1, 3, 5, 7, 8, 10 and 11, which 
contain the basic combinations, will 
become memorized or firmly fixed in the 
mind after sufficient practice. 

Briefly, I want to suggest again; go 
slow at first in giving the sum of each 


CONCLUSION 


59 


combination, in order to be sure you are 
accurate, and endeavor to pass from one 
combination to another in like manner 
as you would pass from word to word in a 
sentence; that is, without hesitation. 
Learn each basic combination so that its 
sum can be given immediately—at a 
glance. Also “think out” what makes 
the answer you arrive at. Alternate this 
method of reading by skipping from one 
combination to another without following 
the present order of the combinations, and 
also orally with the help of an assistant 
as mentioned in the general suggestions. 












































library of congress 



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